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ANALYTICAL MECHANICS
ANGULAR  VELOCITY.
Angular Displacement.—When the motion of a particle Ted to an axis, then the angle which the axial plane, ie plane determined by the particle and the axis, >es, is called an angular displacement. Angular dis-lent is a vector magnitude
is represented by a vector
along the axis; as in the if the vector representation Drque. The directional rela-are the same; that is, the
points towards the observer
considered as positive when tation is counter-clockwise. tits away from the observer
negative when the rotation kwise.
relation between the linear jement of a particle and its
,r displacement about an axis may be found from a eration of Fig. 54:
de=™
r ds cos 0

ds is the linear displacement of the particle P, do is [•responding displacement about an axis through the 9 perpendicular to the plane of the paper, and </> is a;le ds makes with the normal to the axial plane. >n r is constant $ is zero, and the particle describes a in which case the last equation becomes